Relevant bibliographies by topics / Solvable groups

Academic literature on the topic 'Solvable groups'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Journal articles on the topic "Solvable groups":

1

Albrecht, Ulrich. "The construction of $A$-solvable Abelian groups." Czechoslovak Mathematical Journal 44, no. 3 (1994): 413–30. http://dx.doi.org/10.21136/cmj.1994.128480.

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Cherlin, Gregory L., and Ulrich Felgner. "Homogeneous Solvable Groups." Journal of the London Mathematical Society s2-44, no. 1 (August 1991): 102–20. http://dx.doi.org/10.1112/jlms/s2-44.1.102.

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Atanasov, Risto, and Tuval Foguel. "Solitary Solvable Groups." Communications in Algebra 40, no. 6 (June 2012): 2130–39. http://dx.doi.org/10.1080/00927872.2011.574241.

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Sarma, B. K. "Solvable fuzzy groups." Fuzzy Sets and Systems 106, no. 3 (September 1999): 463–67. http://dx.doi.org/10.1016/s0165-0114(97)00264-9.

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Ray, Suryansu. "Solvable fuzzy groups." Information Sciences 75, no. 1-2 (December 1993): 47–61. http://dx.doi.org/10.1016/0020-0255(93)90112-y.

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Chen, P. B., and T. S. Wu. "On solvable groups." Mathematische Annalen 276, no. 1 (March 1986): 43–51. http://dx.doi.org/10.1007/bf01450922.

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Abobala, Mohammad, and Mehmet Celik. "Under Solvable Groups as a Novel Generalization of Solvable Groups." Galoitica: Journal of Mathematical Structures and Applications 2, no. 1 (2022): 14–20. http://dx.doi.org/10.54216/gjmsa.020102.

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The objective of this paper is to define a new generalization of solvable groups by using the concept of power maps which generalize the classical concept of powers (exponents). Also, it presents many elementary properties of this new generalization in terms of theorems.
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GRUNEWALD, FRITZ, BORIS KUNYAVSKII, and EUGENE PLOTKIN. "CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL." International Journal of Algebra and Computation 23, no. 05 (August 2013): 1011–62. http://dx.doi.org/10.1142/s0218196713300016.

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We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.
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ZARRIN, MOHAMMAD. "GROUPS WITH FEW SOLVABLE SUBGROUPS." Journal of Algebra and Its Applications 12, no. 06 (May 9, 2013): 1350011. http://dx.doi.org/10.1142/s0219498813500114.

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In this paper, we give some sufficient condition on the number of proper solvable subgroups of a group to be nilpotent or solvable. In fact, we show that every group with at most 5 (respectively, 58) proper solvable subgroups is nilpotent (respectively, solvable). Also these bounds cannot be improved.
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Khazal, R., and N. P. Mukherjee. "A note onp-solvable and solvable finite groups." International Journal of Mathematics and Mathematical Sciences 17, no. 4 (1994): 821–24. http://dx.doi.org/10.1155/s0161171294001158.

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The notion of normal index is utilized in proving necessary and sufficient conditions for a groupGto be respectively,p-solvable and solvable wherepis the largest prime divisor of|G|. These are used further in identifying the largest normalp-solvable and normal solvable subgroups, respectively, ofG.
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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Solvable groups":

1

Bissler, Mark W. "Character degree graphs of solvable groups." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153.

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Wetherell, Chris. "Subnormal structure of finite soluble groups." View thesis entry in Australian Digital Theses Program, 2001. http://thesis.anu.edu.au/public/adt-ANU20020607.121248/index.html.

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Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their Lp compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.
4

Bleak, Collin. "Solvability in groups of piecewise-linear homeomorphisms of the unit interval." Diss., Online access via UMI:, 2005.

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Vershik, A. M., and Andreas Cap@esi ac at. "Geometry and Dynamics on the Free Solvable Groups." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi899.ps.

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Roth, Calvin L. (Calvin Lee). "Example of solvable quantum groups and their representations." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28104.

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Yang, Yong. "Orbits of the actions of finite solvable groups." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024783.

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Dugan, Carrie T. "Solvable Groups Whose Character Degree Graphs Have Diameter Three." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573.

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Vassileva, Svetla. "The word and conjugacy problems in classes of solvable groups." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66827.

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This thesis is a survey of certain algorithmic problems in group theory and their computational complexities. In particular, it consists of a detailed review of the decidability and complexity of the word and conjugacy problems in several classes of solvable groups, followed by two original results. The first result states that the Conjugacy Problem in wreath products which satisfy certain elementary conditions is decidable in polynomial time. It is largely based on work by Jane Matthews, published in 1969. The second result, based on ideas of Remeslennikov and Sokolov (1970), and Myasnikov, Roman'kov, Ushakov and Vershik (2008) gives a uniform polynomial time algorithm to decide the Conjugacy Problem in free solvable groups.
Cette thèse est une synthèse de certains problèmes algorithmiques dans la thèoriedes groupes et leur complexité computationnelle. Plus particulièrement, elle présenteune revue détaillée de la décidabilité et de la complexité des problèmes du mot et dela conjugaison dans plusieurs classes de groupes solubles, suivie de deux nouveauxrésultats. Le premier résultat énonce que le problème de la conjugaison dans lesproduits couronne qui satisfont certaines conditions élémentaires est décidable entemps polynomial. Elle part d'une publication de Jane Matthews (1969). Le deuxièmerésultat, basé sur des idées de Remeslennikov et Sokolov (1970) et de Myasnikov, Roman'kov,Ushakov et Vershik (2008), présente un algorithme en temps polynomial uniformepour décider le problème de conjugaison dans les groupes solubles libres.
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Sass, Catherine Bray. "Prime Character Degree Graphs of Solvable Groups having Diameter Three." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1398110266.

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Books on the topic "Solvable groups":

1

Manz, Olaf. Representations of solvable groups. Cambridge: Cambridge University Press, 1993.

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2

Doerk, Klaus. Finite soluble groups. Berlin: W. de Gruyter, 1992.

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3

Shunkov, V. P. O vlozhenii primarnykh ėlementov v gruppe. Novosibirsk: VO Nauka, 1992.

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Shunkov, V. P. Mp̳-gruppy. Moskva: "Nauka", 1990.

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5

Short, M. W. The primitive soluble permutation groups of degree less than 256. Berlin: Springer-Verlag, 1992.

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6

Abels, Herbert. Finite presentability of S-arithmetic groups: Compact presentability of solvable groups. Berlin: Springer-Verlag, 1987.

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Segal, Daniel. Words: Notes on verbal width in groups. Cambridge: Cambridge University Press, 2009.

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Bencsath, Katalin A. Lectures on Finitely Generated Solvable Groups. New York, NY: Springer New York, 2013.

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Bencsath, Katalin A., Marianna C. Bonanome, Margaret H. Dean, and Marcos Zyman. Lectures on Finitely Generated Solvable Groups. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-5450-2.

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Fujiwara, Hidenori, and Jean Ludwig. Harmonic Analysis on Exponential Solvable Lie Groups. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55288-8.

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Book chapters on the topic "Solvable groups":

1

Sury, B. "Solvable groups." In Texts and Readings in Mathematics, 63–74. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-19-4_2.

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Brzeziński, Juliusz. "Solvable Groups." In Springer Undergraduate Mathematics Series, 73–75. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72326-6_12.

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Escofier, Jean-Pierre. "Solvable Groups." In Graduate Texts in Mathematics, 195–206. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0191-2_11.

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Borel, Armand. "Solvable Groups." In Graduate Texts in Mathematics, 111–46. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0941-6_4.

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Ceccherini-Silberstein, Tullio, and Michele D’Adderio. "Solvable Groups." In Springer Monographs in Mathematics, 59–72. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-88109-2_4.

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Springer, T. A. "Solvable F-groups." In Linear Algebraic Groups, 238–51. Boston, MA: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4840-4_14.

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Kirillov, A. "Solvable Lie groups." In Graduate Studies in Mathematics, 109–34. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/064/04.

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Myasnikov, Alexei, Vladimir Shpilrain, and Alexander Ushakov. "Free solvable groups." In Non-commutative Cryptography and Complexity of Group-theoretic Problems, 285–307. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/surv/177/19.

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San Martin, Luiz A. B. "Solvable and Nilpotent Groups." In Lie Groups, 199–210. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7_10.

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Machì, Antonio. "Nilpotent Groups and Solvable Groups." In UNITEXT, 205–52. Milano: Springer Milan, 2012. http://dx.doi.org/10.1007/978-88-470-2421-2_5.

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Conference papers on the topic "Solvable groups":

1

RHEMTULLA, AKBAR, and HOWARD SMITH. "ON INFINITE SOLVABLE GROUPS." In Proceedings of the AMS Special Session. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814503723_0010.

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Watrous, John. "Quantum algorithms for solvable groups." In the thirty-third annual ACM symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/380752.380759.

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Luks, E. M. "Computing in solvable matrix groups." In Proceedings., 33rd Annual Symposium on Foundations of Computer Science. IEEE, 1992. http://dx.doi.org/10.1109/sfcs.1992.267813.

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Kahrobaei, Delaram. "Doubles of Residually Solvable Groups." In A Festschrift in Honor of Anthony Gaglione. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793416_0013.

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Eskin, Alex, and David Fisher. "Quasi-isometric Rigidity of Solvable Groups." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0092.

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Li, Xianhua. "On Some Results of Finite Solvable Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0029.

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Omer, S. M. S., N. H. Sarmin, and A. Erfanian. "The orbit graph for some finite solvable groups." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882585.

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Ballesteros, A., A. Blasco, and F. Musso. "Lotka-Volterra systems as Poisson-Lie dynamics on solvable groups." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733365.

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BARBERIS, MARÍA LAURA. "HYPERCOMPLEX STRUCTURES ON SPECIAL CLASSES OF NILPOTENT AND SOLVABLE LIE GROUPS." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0001.

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Markon, Sandor. "A solvable simplified model for elevator group control studies." In 2015 IEEE 4th Global Conference on Consumer Electronics (GCCE). IEEE, 2015. http://dx.doi.org/10.1109/gcce.2015.7398739.

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